MinT - Best Known (87−25, 87, s)-Nets in Base 9

Best Known (87−25, 87, s)-Nets in Base 9

(87−25, 87, 740)-Net over F₉ — Constructive and digital

Digital (62, 87, 740)-net over F₉, using

5 times m-reduction [i] based on digital (62, 92, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 46, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(87−25, 87, 3539)-Net over F₉ — Digital

Digital (62, 87, 3539)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−25, 87, 4560460)-Net in Base 9 — Upper bound on s

There is no (62, 87, 4560461)-net in base 9, because

1 times m-reduction [i] would yield (62, 86, 4560461)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11610 631251 686892 200873 303560 442557 409193 528881 624694 946255 324301 142900 397094 908513 > 9⁸⁶ [i]